DLMF:31.2.E8 (Q8989): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:31.2.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}\zeta}^{2}}+% \left((2\gamma-1)\frac{\operatorname{cn}\zeta\operatorname{dn}\zeta}{% \operatorname{sn}\zeta}-(2\delta-1)\frac{\operatorname{sn}\zeta\operatorname{% dn}\zeta}{\operatorname{cn}\zeta}-(2\epsilon-1)k^{2}\frac{\operatorname{sn}% \zeta\operatorname{cn}\zeta}{\operatorname{dn}\zeta}\right)\frac{\mathrm{d}w}{% \mathrm{d}\zeta}+4k^{2}(\alpha\beta{\operatorname{sn}^{2}}\zeta-q)w=0.}}

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DLMF:31.2.E8

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Jacobian elliptic function

Defining formula

{\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}

C22.S2.E5.m2adec

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Jacobian elliptic function

Defining formula

{\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}

C22.S2.E6.m2adec

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Jacobian elliptic function

Defining formula

{\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}

C22.S2.E4.m2aadec

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derivative of $$f$$ with respect to $$x$$

Defining formula

{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

C1.S4.E4.m2acdec

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Defining formula

{\displaystyle{\displaystyle\gamma}}

C31.S1.XMD10.m1ddec

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Defining formula

{\displaystyle{\displaystyle\delta}}

C31.S1.XMD11.m1ddec

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Defining formula

{\displaystyle{\displaystyle\epsilon}}

C31.S1.XMD12.m1ddec

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Defining formula

{\displaystyle{\displaystyle q}}

C31.S1.XMD7.m1cdec

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Defining formula

{\displaystyle{\displaystyle\alpha}}

C31.S1.XMD8.m1cdec

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